Question: Andrei has a glass tank. First, he wants to put in some marbles, each of which has a volume of $0.04$ liters. Then, he wants to fill the tank with water until it's completely full. If he uses $50$ marbles, he will have to add $33$ liters of water. What is the volume of the tank?
Solution: The volume of each marble is $0.04$ liters, so the volume of $N$ marbles is $0.04N$ liters. The sum of the water's volume and the marbles' volume should be equal to the tank's volume. We can express this with the equation $W+0.04N=T$, where: $W$ represents the volume of water used (in liters) $N$ represents the number of marbles used $T$ represents the tank's volume (in liters) We know that if Andrei uses $50$ marbles $(N={50})$, he will have to add $33$ liters of water $(W={33})$. Let's plug these values into the equation to find the value of $T$. $ T={33}+0.04\cdot{50}=35$ Therefore, the volume of the tank is $35$ liters. To find the number of marbles that corresponds to $20$ liters of water, we can plug $W=20$ into the equation and solve for $N$. $ \begin{aligned}35&=20+0.04N\\ 0.04N&=15\\ N&=375\end{aligned}$ The volume of the tank is $35$ liters. Andrei needs $375$ marbles to fill up the tank with $20$ liters of water.